122 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



micelles are elongated and on an average lie parallel to the length of the 

 fibre; they are, however, tilted to a greater or less degree to this common 

 line of orientation, i.e. they have angular dispersion, and this can be 

 allowed for by allowing the axis Mm to wobble slightly as it rotates. 

 The intersection of the axis with the projection sphere then describes 

 two polar caps limited by two small circles MM' and mm', and the 

 locus of the pole is a family of circles of which two are represented in 



Fig. 42. For explanation, see text. 



Fig. 42(b); the spots are therefore drawn out into two arcs PP, QQ, 

 which are more intense at their centres. 



Now to derive from this construction the pattern to be expected 

 from a set of planes parallel to the cellulose chain direction in a fibre 

 wound with a spiral, one has merely to remember that the spiral is 

 formed in eff"ect by a tilt of the micelles through a constant angle to the 

 longitudinal, in the plane of the fibre wall. Taking any small element 

 of the wall, therefore, the axis of rotation is tilted through some angle 

 S, and the effect may be seen in Fig. 42(b) if a is replaced by S in the 

 diagram. The circle LI, the locus of the pole to which Mm is normal, is 

 tilted through the same angle S, and its intersection with the reflexion 

 circle is therefore depressed. To represent the whole figure the axis 

 Mm is rotated about the direction of the fibre length, the axis traces out 

 the hollow cone MmOM'm', and the locus of the pole P becomes the 

 belt LILT bounded by two broken small circles in Fig. 42(b). The 

 lateral spots are again therefore drawn out into two arcs whose lengths 

 depend on the value of the angle S of the spiral. Clearly, however, the 

 intensity distribution along the arcs will be different from that referred 

 to in the arcs derived above for angular dispersion. The cone 



